Question

A hospital lab is looking at a new diagnostic device with which it will initially take a technician approximately 60 minutes to run a common battery of tests frequently requested by the medical staff. The manufacturer has suggested that a learning curve with a learning rate of 90% may be appropriate for the technician operating the device. The test is requested about 10 times per week.

(a) (3 pts) How many tests would they accumulate over the next six months? What would be the testing time by then?

(b) (3 pts) At the current rate of demand, how long will it take to get the time required for the test to be around 20 minutes?

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Answer 1

a) Time required for first test by the technician: 60 Minutes

No. of tests per week = 10

No. of tests per month = 4 weeks * 10 = 40

Therefore, no. of tests in 6 months = 6 months * 4 weeks * 10 per week = 240

Learning curve is 90% = 90/100 = 0.09

The learning effect would reduce the time required on each test, and the required number of tests at the end of six months would be 240 tests as calculated above.

Now the formula for finding the time required after the learning effect is as follows:

y = ax^b

Where,

y = Average time per unit for x units

a = Time required for first unit

x = Cumulative number of units produced

b = Leaning co efficient = log of Learning rate / Log of 2

Putting the values in formula, we get,

y = 60 * 240^{log 0.9/ log 2,}

From log table we get Log 0.9 = -0.0457 and log 2 = 0.3010

y = 60 *  240 ^{-0.0457/0.3010}

y = 60 * 240 ^-0.1518

From scientfic calculator we can get the value of 240^-0.1518 = 0.4352

y = 60 * 0.4352

y = 26.11

Therefore, time required per test for 240 tests = 26.11 minutes, and total time required for 240 tests = 26.11 * 240 = 6266.4 minutes

b) Time required is given at 20 minutes

number of tests = x, b = -0.1518, y = 20 minutes and a = 60 minutes

putting the values in y = ax^b,

we get 20 = 60 * x ^-0.1518

x^-0.1518 = 20/60

x^-0.1518 = 0.3333

x = ^-0.1518√0.3333 i.e. -0.1518^th root of 0.3333 which we can calculate from scientific calculator,

x = 1391.61 approximately 1392 tests

in our case, it is number of tests required

and 10 tests are performed each week, number of weeks = 1392 / 10 = 139.2 weeks is the time required for the test to be around 20 minutes.